TY - GEN
T1 - Dynamic Approximate Multiplicatively-Weighted Nearest Neighbors
AU - Aronov, Boris
AU - Katz, Matthew J.
N1 - Publisher Copyright: © 2022 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. All rights reserved.
PY - 2022/6/1
Y1 - 2022/6/1
N2 - We describe a dynamic data structure for approximate nearest neighbor (ANN) queries with respect to multiplicatively weighted distances with additive offsets. Queries take polylogarithmic time, while the cost of updates is amortized polylogarithmic. The data structure requires near-linear space and construction time. The approach works not only for the Euclidean norm, but for other norms in Rd, for any fixed d. We employ our ANN data structure to construct a faster dynamic structure for approximate SINR queries, ensuring polylogarithmic query and polylogarithmic amortized update for the case of non-uniform power transmitters, thus closing a gap in previous state of the art. To obtain the latter result, we needed a data structure for dynamic approximate halfplane range counting in the plane. Since we could not find such a data structure in the literature, we also show how to dynamize one of the known static data structures.
AB - We describe a dynamic data structure for approximate nearest neighbor (ANN) queries with respect to multiplicatively weighted distances with additive offsets. Queries take polylogarithmic time, while the cost of updates is amortized polylogarithmic. The data structure requires near-linear space and construction time. The approach works not only for the Euclidean norm, but for other norms in Rd, for any fixed d. We employ our ANN data structure to construct a faster dynamic structure for approximate SINR queries, ensuring polylogarithmic query and polylogarithmic amortized update for the case of non-uniform power transmitters, thus closing a gap in previous state of the art. To obtain the latter result, we needed a data structure for dynamic approximate halfplane range counting in the plane. Since we could not find such a data structure in the literature, we also show how to dynamize one of the known static data structures.
KW - Approximate nearest neighbors
KW - Dynamic data structures
KW - Nearest neighbor queries
KW - Nearest neighbors
KW - SINR queries
KW - Weighted nearest neighbors
UR - http://www.scopus.com/inward/record.url?scp=85133398287&partnerID=8YFLogxK
U2 - https://doi.org/10.4230/LIPIcs.SWAT.2022.11
DO - https://doi.org/10.4230/LIPIcs.SWAT.2022.11
M3 - Conference contribution
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 18th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2022
A2 - Czumaj, Artur
A2 - Xin, Qin
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 18th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2022
Y2 - 27 June 2022 through 29 June 2022
ER -